Object or shape information representation method

ABSTRACT

An information representation method for representing an object or a shape includes: dividing a contour shape of an entirety or a part of the object or the shape into one or a plurality of curves; and representing the contour shape of the object or the shape by parameters including a degree of curvature and a positional relationship of each curve obtained by the dividing. Therefore, there is provided an information representation method for an object or a shape, which is capable of robust object recognition against a change in image by geometric transformations and occlusions.

TECHNICAL FIELD

This invention relates to an information representation method for anobject or a shape.

BACKGROUND ART

In recent years, as digital image devices such as digital cameras haverapidly prevailed, an expectation for generic object recognition forrecognizing what objects are contained in a taken picture image andvideo is increasing. The generic object recognition has a possible usefor various applications such as proper classification of image datastored in a database without being classified, search for necessaryimage data, further, extraction of a desired scene from a motion image,and cutting out only desired scenes to re-edit then.

As technologies for the object recognition, various recognitiontechnologies such as face recognition and fingerprint recognition havebeen developed, and all of them are directed to specific applications.If such a recognition technology specialized in a certain singleapplication is used to another application, there arise such a problemthat a recognition rate immediately decreases and the like. Therefore,development of technologies for recognizing a generic object isexpected.

In order to recognize a generic object, it is necessary to extractfeature amounts of an image subject to recognition. As methods forextracting feature amounts, methods of using geometrical featurescontained in an image, which are described in Patent Literature 1 andPatent Literature 2, are widely known. However, most of those featureamounts cannot be calculated unless parameters such as thresholds areset in advance based on statistical learning or experience of a user. Amethod which requires the statistical learning and the experience of auser cannot calculate a feature amount for an image which has not beenlearned, and poses such a problem that an erroneous recognition resultis provided.

As a method to calculate a feature amount without necessity of thestatistical learning or the experience of a user, a method described inNon Patent Literature 1 and called Scale Invariant Feature Transform(SIFT), which uses a histogram accumulating a local intensity gradientof an image, is widely recognized. By using this technology, the sameimages including geometric transformations and occlusions can berecognized as being the same. However, this technology is intended todetermine whether or not two images are the same, and cannot provideinformation on to what degree two similar image are similar.

Moreover, recognition using a representation method described in NonPatent Literature 2 and called Curvature Scale Space (CSS), whichinvolves smoothing an image contour stepwise and representing the imageby using positions of inflection points of the counter at each step, isalso well known. It is known that position information on the inflectionpoints used in this technology has a very similar appearance pattern forthe same images or similar images. Thus, by using this technology,images same or similar in contour can be recognized, or images obtainedby applying a geometric transformation to the images can be recognizedas the same or similar images. However, this technology does not useinformation on points other than the inflection points at all, but usesonly very limited information out of information on the contours.Therefore, for images similar in contour to each other, if the pieces ofposition information on inflection points are different from each other,it may be determined that the images are not “similar” to each other.Moreover, even for images dissimilar in contour to each other, if piecesof position information on inflection points are relatively similar toeach other, it may be determined that the images are “similar” to eachother. In other words, this technology cannot calculate a degree ofsimilarity based on features in contour.

On the other hand, a method of recognition based on curvatureinformation on respective points on a contour is also proposed (PatentLiterature 3). This technology uses the curvature information on allpoints on the contour, and can calculate a degree of similarity forcontours slightly different in contour shape. However, this technologyassumes comparison in contour for an entire periphery of an outline of ashape. As a result, if a contour is disconnected halfway or a part of anobject shape overlaps another object shape in an image, this technologycannot be used.

CITATION LIST Patent Literature

-   Patent Document 1: Japanese Unexamined Patent Application    Publication (JP-A) 2002-352252-   Patent Document 2: Japanese Unexamined Patent Application    Publication (JP-A) 2005-346391-   Patent Document 3: Japanese Unexamined Patent Application    Publication (JP-A) 10-055447

NON PATENT LITERATURE

-   Non-Patent Document 1: Lowe, D. G, Object recognition from local    scale invariant features, Proc. of IEEE International Conference on    Computer Vision, pp. 1150-1157-   Non-Patent Document 2: FARZIN MOKHTARIAN AND ALAN MACKWORTH,    Scale-based description and Recognition of Planar curves and    two-dimensional spaces, IEEE Transactions on Pattern Analysis and    Machine Intelligence Vol. 8, No. 1, pp. 34-43

DISCLOSURE OF THE INVENTION

The conventional object recognition methods determine, based on thestatistical learning and experience of a user, parameters forcalculating feature amounts to be extracted. As a result, it is hard torecognize an image which has not been learnt. On the other hand, themethod of calculating a feature amount without necessity of thestatistical learning or the experience of a user has such a problemthat, when a shape to be recognized does not have a complete contour, adegree of similarity having enough information is difficult tocalculate.

It is therefore an object of this invention to provide an informationrepresentation method for an object or a shape, which is capable ofdetermining a degree of similarity representing to what degree twodifferent images are similar to each other, and of robust objectrecognition against a change in image by geometric transformations andocclusions.

According to one mode of this invention, there is provided aninformation representation method for representing an object or a shape,including: dividing a contour shape of an entirety or a part of theobject or the shape into one or a plurality of curves; and representingthe contour shape by parameters including a degree of curvature and apositional relationship of each curve obtained by the dividing.

An effect of the one mode of this invention is to provide an approach ofrecognizing a generic object without necessity of the statisticallearning and the experience of a user. In particular, for shapes thatgenerally exist, such as shapes which are similar but different indetail such as hand writings, object shapes of which it is difficult toextract entire contours from background information, object shapes ofwhich it is difficult to extract entire contours due to a lack of partsof shapes because of occlusions and other such reasons, and objectshapes of which it is difficult to extract entire contours due todiscontinuity inside shapes, a method for robust recognition isprovided.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a block diagram illustrating a schematic configuration of animage processing device according to a first embodiment of thisinvention.

FIG. 2 is a view illustrating an example of an image represented byimage information acquired by an image information acquisition unitincluded in the image processing device of FIG. 1.

FIG. 3 is a view illustrating an example of contour lines represented bycontour information extracted by a contour extraction unit included inthe image processing device of FIG. 1.

FIG. 4 is a view illustrating an example of the contour line smoothed toa certain smoothing level.

FIG. 5 is a view illustrating an example of smoothing the contour lineillustrated in FIG. 4 to a higher smoothing level.

FIG. 6 is a view illustrating an example of smoothing the contour lineillustrated in FIG. 5 to a higher smoothing level.

FIG. 7 is a diagram illustrating geometric transformations.

FIG. 8 is a table illustrating an example of information output by acontour arc length/curvature/position output unit included in the imageprocessing device of FIG. 1.

FIGS. 9A and 9B are diagrams illustrating an example of two contourlines subject to determination for similarity/dissimilarity in the imageprocessing device of FIG. 1.

FIGS. 10A and 10B are graphs respectively illustrating results ofprofiling of arc length information and curvature information acquiredfrom the contour lines of FIGS. 9A and 9B.

FIG. 11 is a diagram illustrating an example of smoothing contour linesof numbers in two types of fonts at a plurality of stages.

FIG. 12 is a flowchart illustrating an example of an operation of theimage processing device of FIG. 1.

FIG. 13 is a block diagram illustrating a schematic configuration of animage processing device according to a second embodiment of thisinvention.

FIG. 14 is a diagram illustrating a characteristic area of a dividedcontour line.

FIG. 15 is a flowchart illustrating an example of an operation of theimage processing device of FIG. 13.

FIG. 16 is a block diagram illustrating a schematic configuration of animage processing device according to a third embodiment of thisinvention.

FIG. 17 is a flowchart illustrating an example of an operation of theimage processing device of FIG. 16.

BEST MODE FOR EMBODYING THE INVENTION

A detailed description is now given of embodiments of this inventionreferring to drawings.

The representation method of representing an object or a shape accordingto a first embodiment of this invention is realized by, for example, animage processing device illustrated in FIG. 1.

The image processing device of FIG. 1 includes a control unit 10, amemory 20, an input/output unit 30, an image information acquisitionunit 101, a contour extraction unit 102, a contour smoothing unit 103, acontour division unit 104, a contour arc length calculation unit 105, acontour curvature calculation unit 106, a contour position calculationunit 107, a contour arc length/curvature/position output unit 108, animage determination unit 109, an image information storage unit 201, anda contour arc length/curvature/position information storage unit 202.

The image information acquisition unit 101 picks out image information(image data) such as a photograph specified by a user with theinput/output unit 30, from the image information storage unit 201.Alternatively, the image information acquisition unit 101 may acquireimage information from an image input unit (not shown) such as ascanner. The image information acquisition unit 101 may carry outconversion processing for facilitating subsequent processing when theimage information is acquired, such as color/black and white conversion.FIG. 2 illustrates an example of an image represented by the imageinformation acquired by the image information acquisition unit 101. Theimage in FIG. 2 includes only one object (dog).

The contour extraction unit 102 extracts contour information (contourlines) of objects included in the image from the image informationacquired by the image information acquisition unit 101. The contourinformation can be extracted by extracting points at which the hue, thechroma, the lightness, and the like change sharply by means of theLaplacian of Gaussian filter, for example. Of course, the method ofextracting contour information is not limited to the above-mentionedmethod. The extracted contour information of the object is representedby a set of contour points represented as (x, y) by the Cartesiancoordinate system, or the like. FIG. 3 illustrates an example of contourlines represented by the contour information extracted by the contourextraction unit 102.

The contour smoothing unit 103 carries out stepwise multiple-stagesmoothing on the contour lines extracted by the contour extraction unit102. For the smoothing, convolution by means of the Gaussian filter, forexample, can be used, but the means for the smoothing is not limited tothe convolution. The smoothing is carried out in order to first removeinfluence of noise on subsequent processing, and is carried out tosubsequently acquire a plurality of pieces of stepwise (stratified)contour information (smoothed contour lines). As described later, byacquiring, for each of the plurality of pieces of stepwise contourinformation, a degree of similarity to pieces of stepwise contourinformation acquired for an object in another image, the degree ofsimilarity of the shapes of the objects can be acquired at a higheraccuracy. A degree of smoothing (smoothing level) is determined based onthe number of times of the smoothing or the number of “inflectionpoints” to be described later. FIGS. 4 to 6 illustrate an example of themulti-stage (hierarchical) smoothing based on the number of theinflection points as a guideline. The number of “inflection points”decreases as a result of repetition of the smoothing, and is finallyconverged to zero (any contour of a closed surface becomes a convexgraphic after the smoothing level reaches a certain degree or higher).

The smoothing is required if the hierarchizing is carried out by meansof the smoothing, but the smoothing is not necessarily required if thehierarchizing is carried out by means of another method.

The contour division unit 104 functions as division means for dividingthe contour line at each of the smoothing levels smoothed by the contoursmoothing unit 103 into one or more partial contour lines. The divisionis carried out while points characteristic in degree of curvature in thesmoothed contour line are considered as division points. As a result ofthe use of such division points, the partial contour line becomes acurved line. If there is no division point, the division is not carriedout. In this case, the divided contour line after the division matchesthe entire contour line before the division. In this way, the contourshape of the entirety or a part of the object or the shape is dividedinto one or a plurality of curved lines.

On this occasion, the “degree of curvature” is an amount defined basedon a characteristic relating to the curvature of the curved line such asthe Euclidian curvature, the Euclidian radius of curvature, or theaffine curvature, and is an amount describing to what degree the curvedline is distorted compared with a straight line. Any one of thoseamounts may be used as the amount defining the degree of curvature ofthe curved line, and the Euclidian curvature is used on this occasion.In other words, the contour division unit 104 divides the contour linewhile the inflection points in the Euclidian curvature on the contourline are considered as division points.

Moreover, the “inflection point” means a point at which the sign of thecurvature changes on the contour line. The inflection point in theEuclidian curvature is invariant with respect to projectiontransformation, and is thus a point robust against the geometrictransformation. In other words, by using the inflection points in theEuclidian curvature as division points, points robust against thegeometric transformation can be set as division points.

On this occasion, referring to FIG. 7, a description is given of thegeometric transformations. In FIG. 7, “transformation group” is a groupincluding each of geometric transformations as an element. Asappreciated from FIG. 7, the Euclidian geometric transformations(including rotations) are transformations including rotations andtranslations. Moreover, the affine geometric transformations (includingsimilarity transformations) are transformations obtained by addingscaling/shearing transformations to the Euclidian geometrictransformations. In addition, projective transformations are obtained byadding the fan-shaped transformations to the affine transformations.Thus, a relationship: (projective transformations)

(affine transformations)

(Euclidian transformations) is established, and the projectivetransformations are geometric transformations in the broadest sense outthereof The inflection point in the Euclidian curvature is an invariablewith respect to the projective geometric transformations, and can beconsidered to be robust in the geometric transformations in the broadestsense. In other words, if the inflection point in the Euclidiancurvature is set to a division point, the division point is a divisionpoint robust against the geometric transformations.

A description is now given of the division method for a contour linewhile inflection points in the Euclidian curvature are division points.

First, one arbitrary point is set as a start point, and coordinates t ofcontour points are selected so as to go around the contour line. At eachof the contour points, a Euclidian curvature κ(t) defined by thefollowing Equation (1) is calculated, and points having a value of theEuclidian curvature of zero are extracted as division points of thecontour.

$\begin{matrix}{{\kappa (t)} = \frac{{\overset{.}{x}\overset{¨}{y}} - {\overset{.}{y}\overset{¨}{x}}}{\left( {{\overset{.}{x}}^{2} + {\overset{.}{y}}^{2}} \right)^{2/3}}} & (1)\end{matrix}$

On this occasion, □ and □ respectively represent a first orderderivative and a second order derivative of x with respect to t. Thesame holds true for □ and □.

As described above, before the contour line is divided by the contourdivision unit 104, as preprocessing thereof, it is preferred to carryout the smoothing to a certain degree. With the smoothing as thepreprocessing, the contour line can be divided without influence of adegree of local curvature when noise is high. Moreover, the division ofthe contour line is carried out for smoothed contour lines at all thesmoothing levels obtained by the plurality of stages of smoothing. Ifthe length of the contour line is not enough for subsequent processing,the entire contour line may be considered as a divided contour line, andthe division may not be carried out further.

The division method for the contour line by using inflection points inthe Euclidian curvature has been described above, but the divisionmethod for the contour is not limited to this method.

The contour arc length calculation unit 105 calculates an arc length ofeach of the divided contour lines divided by the contour division unit104. On this occasion, the arc length may be any of the Euclidian arclength and the affine arc length, but the affine arc length ispreferably used. The affine arc length is an invariable with respect tothe equivalent affine geometric transformations (including the Euclidiangeometric transformations), and is thus a more robust amount withrespect to the geometric transformations. The affine arc length s isdefined by the following Equation (2).

s=∫ _(t) ₁ ^(t) ₂ det(p′(t)p″(t))⅓dt   (2)

On this occasion, t₁ and t₂ respectively represent coordinates of astart point and an end point of each of the divided contour lines. Notethat, the start point and the end point are points which can bedetermined by a shape of the divided contour line.

The contour curvature calculation unit 106 calculates a curvature ofeach of the divided contour lines divided by the contour division unit104. On this occasion, the curvature may be any of the Euclidiancurvature and the affine curvature, but the affine curvature ispreferably used. The affine curvature is an invariable with respect tothe equivalent affine geometric transformations including the equivalentEuclidian geometric transformations, and is thus a more robust amountwith respect to the geometric transformations. The affine curvatureκ_(A) is defined by the following Equation (3).

κ_(A)(s(t)0=det(p″(s(t))p″(s(t)))   (3)

On this occasion, p denotes a coordinate vector

${p = \begin{pmatrix}x \\y\end{pmatrix}},$

and p″ and p′″ respectively represent a second order derivative and athird order derivative of p with respect to s.

The curvature information calculated by the contour curvaturecalculation unit 106 may define curvature information on all contourpoints included in the divided contour line as a vector having as manydimensions as the number of the contour points, or may be represented byvalues such as an average value, or the maximum/minimum values. Both thearc length and the curvature of the divided contour line are invariableswith respect to the equivalent affine transformations, and an effectbrought about by determining both the arc length and the curvature ofthe divided contour line is thus to provide invariables with respect tothe affine geometric transformation accompanying scaling by taking aratio of one to the other thereof Note that, the contour point is apoint which can be determined by the shape of the divided contour line.

Both the arc length information calculated by the contour arc lengthcalculation unit 105 and the curvature information calculated by thecontour curvature calculation unit 106 are feature amounts (parameters)representing the degree of curvature of a corresponding divided contourline, and as a result, a feature of a contour is represented by theparameters. In this way, the contour arc length calculation unit 105 andthe contour curvature calculation unit 106 respectively function asparameter calculation means.

The contour position calculation unit 107 calculates a position (alsoreferred to as positional relationship) of each of the divided contourlines divided by the contour division unit 104. On this occasion, as theposition, coordinates of the inflection points on the both ends of thedivided contour line or coordinates of a center of gravity calculated bythe respective contour point coordinates forming the divided contourline may be used. As the coordinates, in addition to the coordinates inthe Cartesian coordinate system, various coordinates such as thecoordinates in the polar coordinate system may be used. The use of thepolar coordinate system can enable to represent, in addition to thepositional relationship including a size, a positional relationship by arelative angle.

Alternatively, numbers assigned clockwise or counterclockwise insequence along the contour line may be employed as the information onthe position.

Further, as the information on the position of the divided contour line,in addition to the absolute position or the relative position of thedivided contour line, the direction toward which a protruded portion ofthe divided contour line is directed may be included. The direction isdescribed as a direction of a major axis or a minor axis when therespective points included in the divided contour line are approximatedby means of the elliptical approximation. The method of describing thedirection is not limited to the method by means of the ellipticalapproximation, and various approaches such as a method of describing thedirection as a direction orthogonal to a line connecting the positionsof the two end points of the divided contour line with each other can beconceived. Moreover, in addition to the approaches of determining thedirection in this way, an approach of describing (with respect to theentire contour line) the direction as a simple protrusion or recess canbe conceived.

The position calculation by the contour position calculation unit 107can be used to determine a mutual positional relationship betweendivided contour lines relating to one object. Moreover, the positioncalculation can also be used to determine a mutual positionalrelationship of a plurality of contour lines included in one image. Byobserving the positional relationship among the plurality of contourlines, an object can be more precisely recognized, and moreover, even ifa contour line represents a part of an object, the object can berecognized. Further, the position calculation is effective for a casewhere a plurality of contour lines are extracted for a single object.

The contour arc length/curvature/position output unit 108 outputs thearc length information, the curvature information, and the positioninformation respectively calculated by the contour arc lengthcalculation unit 105, the contour curvature calculation unit 106, andthe contour position calculation unit 107 as pieces of informationrepresenting the feature amounts of each of the divided contour lines tothe contour arc length/curvature/position information storage unit 202.FIG. 8 illustrates an example of the information output by the contourarc length/curvature/position output unit 108.

In FIG. 8, a contour line to which an image identifier F1 is assigned isa contour line having a number N1 of inflection points as a result ofthe smoothing, and is divided into three divided contour lines C1-C3.The divided contour line C1 has an arc length S1, a curvature K1, an Xcoordinate X1, a Y coordinate Y1, and a direction D1. The same holdstrue for the divided contour lines C2 and C3.

The image determination unit 109 determines, based on the information(feature amounts) stored in the contour arc length/curvature/positioninformation storage unit 202, match or similarity of two objects(images). The determination can be used to search for an object mostsimilar to one object. Moreover, the determination can be used, in orderto classify one object to any of a plurality of groups, to compare theone object to an object representing each of the groups. In any case,the image determination unit picks out information on one object andinformation on an object for comparison, which is different from the oneobject, from the contour arc length/curvature/position informationstorage unit 202, and compares these pieces of information with eachother, to thereby determine the match/mismatch(similarity/dissimilarity). The determination by the image determinationunit 109 is carried out by comparing pieces of information on the arclength, the curvature, the position, and the direction in entirety or inpart with each other. When a difference (distance in a parameter) in avalue represented by each piece of the information or a value determinedfrom these pieces of information is less than a threshold determined inadvance, the image determination unit 109 determines that these piecesof information “match (similar to) each other”, and otherwise determinesthat these pieces of information “do not match (are not similar to) eachother”.

Referring to FIGS. 9A, 9B, 10A, and 10B, a specific description is givenof a method of determining similarity/dissimilarity between two contourlines. On this occasion, as the two contour lines, two contour linesrepresenting number “5” in fonts different from each other areexemplified.

FIGS. 9A and 9B illustrate contour lines of the number “5” in the fontsdifferent from each other and inflection points on the contour lines.The contour lines are divided into a plurality of divided contour lines,and the arc length information and the curvature information areobtained from each of the divided contour lines. Then, the obtained arclength information and curvature information are profiled, and profilesrespectively illustrated in FIGS. 10A and 10B are acquired. In FIGS. 10Aand 10B, the horizontal axis represents an accumulated length of the arclengths of the divided contour lines, and the vertical axis representsthe curvature corresponding to the respective divided contour lines.

A difference between the thus-obtained profiles of the two contour linesis determined. The difference can be obtained, for example, as a resultof determining and summing a difference in curvature when lengthscorresponding to accumulated arc lengths are equal to each other foraccumulated lengths corresponding to the entire arc lengths. Bycomparing the difference obtained in this way with a threshold set inadvance, the similarity/dissimilarity of the two contour lines isdetermined

The above-mentioned example is described for the case where each of thetwo contour lines subject to the determination represents the entiresingle object, but the determination can be made even if at least one ofthe two contour lines subject to the determination represents a part ofa single object. This is because, according to this embodiment, thecontour division unit 104 divides a contour line into one or morepartial contour lines, and for each of the partial contour lines, therespective pieces of information on the arc length, curvature, position,and the direction are determined Thus, according to this embodiment, thedetermination can be made also for an occluded object or shape.

Moreover, in the above-mentioned example, the example in which thesimilarity/dissimilarity is determined by using the arc lengthinformation and the curvature information on all the plurality ofdivided contour lines has been described, but thesimilarity/dissimilarity may be determined by using the arc lengthinformation and the curvature information on a part of the plurality ofdivided contour lines. In this case, for example, for two contour linesto be compared, a predetermined number of divided contour lines areselected in a descending order of the arc length, and a difference incurvature is determined for each pair of divided contour lines havingthe same positions in order. Then, each of the determined differences incurvature is weighted depending on the order of the arc length, and theweighted differences in curvature are summed Based on the sum obtainedin this way, the similarity/dissimilarity of the two contour lines isdetermined According to this method, the entire information does notneed to be used, resulting in a reduction in an amount of computation,and in high-speed processing.

The above-mentioned determination is carried out for each of thesmoothing levels. As described above, the contour line of each of theobjects is smoothed at the plurality of smoothing levels, and thefeature amounts are determined for the smoothed contour lines at therespective smoothing levels. By making the comparison in the featureamounts for each of the levels from the highest level to the lowestlevel of the smoothing, the degree of similarity in shape between theobjects is determined

If the smoothing level increases, all the graphics (contour lines)converge to convex graphics. Therefore, as the smoothing levelincreases, a possibility of determining that the shapes of the twoobjects “match (are similar to) each other” increases. Thus, dependingon at which smoothing level such a determination that the two objects“match (are similar to) each other” is made, the degree of similaritybetween the shapes of the two objects can be represented. For example,it is determined that contour lines for the same single object “match(are similar to) each other” at all the smoothing levels. Moreover, itis determined that contour lines for very similar objects “match (aresimilar to) each other” on stages starting from a relatively lowsmoothing level. Moreover, it is determined that shapes of objectssimilar to each other to a certain degree “match (are similar to) eachother” when the smoothing level increases. Then, it is determined thatshapes of objects which are not similar at all “do no match (are notsimilar to) each other” even when the smoothing level increases. In thisway, by employing the smoothing levels at the plurality of stages, itcan be determined which image is “similar to” which image to whatdegree.

FIG. 11 illustrates an example of the smoothing on a plurality of stagesapplied respectively to numbers “4”, “7”, and “3” in two types of fontsA and B. The number of the smoothing levels is six, and the smoothinglevel increases from the left to the right in the drawing.

A determination result of the similarity/dissimilarity of each of thenumbers can vary depending on used feature amounts and set thresholds,but the following determination result is obtained, for example.

At the smoothing levels 5 and 6 (first and second columns from the rightin the figure), all the numbers are determined to be “similar” to eachother.

At the smoothing level 4 (third column from the right in the figure),the number “4” and each of the numbers “7” and “3” are determined to be“dissimilar” to each other.

At the smoothing level 3 (third column from the left in the figure), thenumbers “7” and “3” are determined to be “dissimilar” to each other.

At the smoothing level 1 (first column from the left in the figure), thenumbers “4” in the fonts A and B and the numbers “3” in the fonts A andB are determined to be “dissimilar” to each other.

As a result, if the degree of similarity is represented by the smoothinglevels 1-6, the degree of similarity of the numbers “7” in the fonts Aand B is “1”, and the degree of similarity of the numbers “4” in thefonts A and B, and the degree of similarity of the numbers “3” in thefonts A and B are “2”. Moreover, regardless of the fonts, the degree ofsimilarity of the numbers “7” and “3” is “4”, and the degree ofsimilarity of the numbers “4” and “7” and the degree of similarity ofthe numbers “4” and “3” are “5”.

As described above, the image determination unit 109 can determine, bydetermining the similarity/dissimilarity of two contour lines forrespective smoothing levels, a degree of similarity representing to whatdegree the contour lines are similar.

Note that, the determination of the degree of similarity by the imagedetermination unit 109 is not necessarily made by means of thesmoothing. For example, the smoothing can be replaced by an approach ofcomparing, on a plurality of stages, partial contours long in arclength, or partial contours specific to a certain graphic.

A description is now given of an operation example of the imageprocessing device of FIG. 1.

FIG. 12 is a flowchart illustrating an example of an operation of theimage processing device of FIG. 1. As illustrated, first, the imageinformation acquisition unit 101 of the image processing device acquiresimage information specified by a user (Step S1001). The acquisition ofthe image information is not limited to the specification by the user,and the image information may be automatically acquired. For example,depending on a detection result of a sensor or the like, an image isacquired from imaging means.

Then, the image information acquisition unit 101 checks whether allspecified pieces of image information have been acquired (Step S1002).If the acquisition is not complete for all the specified pieces of imageinformation (NO in Step S1002), the image information acquisition unit101 repeats Steps S1001 and S1002 until all the specified pieces ofimage information are acquired. When all the specified pieces of imageinformation have been acquired (YES in Step S1002), the imageinformation acquisition unit 101 sends the acquired image information tothe contour extraction unit 102.

The contour extraction unit 102 extracts contour information included inthe image based on the image information sent from the image informationacquisition unit 101 (Step S1003). The extraction of the contourinformation can be carried out only for contour lines that satisfypredetermined criteria set by the user in advance such as contour lineshaving a length longer than a threshold. The contour informationextracted by the contour extraction unit 102 is sent to the contoursmoothing unit 103.

Then, the contour smoothing unit 103 smoothes a contour line based onthe contour information from the contour extraction unit 102 (StepS1004). The contour smoothing unit 103 detects the number of inflectionpoints (Step S1005), and determines whether or not the number ofinflection points is decreased to a number (corresponding to a certainsmoothing stage) set in advance (Step S1006). The smoothing is repeateduntil the number of inflection points matches (is decreased to) thenumber set in advance. In order to carry out the smoothing on aplurality of stages, the number set in advance used in Step S1006 is avalue which is different depending on the smoothing level.

The contour division unit 104 divides a contour line smoothed on acertain stage into one or more divided contour lines (Step S1007). Thisdivision is carried out while points characteristic in degree ofcurvature in the smoothed contour line are considered as divisionpoints.

For each of the divided contour lines divided by the contour divisionunit 104, the contour arc length calculation unit 105 calculates an arclength (Step S1008), the contour curvature calculation unit 106calculates a curvature (Step S1009), and the contour positioncalculation unit 107 calculates a position (Step S1010).

The contour arc length/curvature/position output unit 108 outputs thearc length/curvature/position information calculated in Steps S1005 toS1007 to the contour arc length/curvature/position information storageunit 202, thereby controlling the contour arc length/curvature/positioninformation storage unit 202 to store the arc length/curvature/positioninformation (Step S1011).

Thereafter, or in parallel with Steps S1007-S1011, the contour smoothingunit 103 determines whether or not the number of the inflection pointsreaches zero or a number equal to or less than the number specified inadvance (S1012). In other words, the contour smoothing unit 103determines, for all the plurality of stages, whether or not a smoothedcontour line is obtained. When a smoothed contour line is not obtainedfor all the smoothing levels, the contour smoothing unit 103 returns toStep S1004, and repeats the subsequent processing.

Then, the contour extraction unit 102 determines whether or not all thecontour lines included in the image information from the imageinformation acquisition unit 101 are extracted (Step S1013). This isprocessing for a case where there are a plurality of contour lines, inparticular, a case where a single object has a plurality of contourliens (a single object is constituted by a plurality of parts). Whenthere are contour lines which have not been extracted, Steps S1003-S1013are repeated.

When, in Step S1013, the result of the determination is YES, the imagedetermination unit 109 determines, based on the information stored inthe contour arc length/curvature/position information storage unit 202,whether or not a certain image and one or more other images are similarto each other. The determination is carried out for each of thesmoothing levels.

For example, when an image most similar to a certain image (search keyimage) is searched from a plurality of images (images subject to thesearch), information on the search key image and the information on theimages subject to the search stored in the contour arclength/curvature/position information storage unit 202 are compared.

First, pieces of information obtained from contour lines lowest indegree of smoothing (in the highest layer) for the respective images arecompared with each other (Step S1014). When pieces of informationmatching (or similar to) each other exist (YES in Step S1015), the imagedetermination unit 109 outputs a searched image corresponding to theinformation as a similar image (Step S1017).

When matching (or similar) information does not exist (NO in StepS1015), the image determination unit 109 compares pieces of informationobtained from contour lines at a smoothing level one stage higher (in alayer one stage lower) with each other (Step S1016). When pieces ofinformation matching (or similar to) each other exist (YES in StepS1015), the image determination unit 109 outputs a searched imagecorresponding to the information as a similar image (Step S1017). Whenmatching (or similar) information does not exist (NO in Step S1015), theimage determination unit 109 compares pieces of information obtainedfrom contour lines at a smoothing level one stage higher with each other(Step S1016). Subsequently, until the image determination unit 109determines that matching (or similar) information exists, or finishesthe determination for the highest degree of smoothing level, StepsS1015-S1016 are repeated.

The description has been given of the case where the most similar imageis output, but the search result may be output as a degree ofsimilarity. In this case, by preparing as the images subject to thesearch representative images (determination criterion images) of aplurality of types of groups, to which group the search key imagebelongs and to what degree the search key image is similar can be outputresults.

As described above, according to this embodiment, by dividing each of aplurality of smoothed contour lines smoothed on a plurality of stagesinto one or more curves, representing each of the divided curves by theparameters including the degree of curvature and the positionalrelationship, and comparing the parameters (feature amounts) at each ofthe smoothing levels, the similarity of two images can be properlyevaluated.

Moreover, by representing the plurality of divided contour lines by theparameters (determining feature amounts for each of the divided contourlines), image recognition robust against the occlusion can be carriedout.

Further, by properly selecting the division points and the featureamounts, image recognition robust against the geometric transformationcan be carried out.

A detailed description is now given of an image processing deviceaccording to a second embodiment of this invention used for realizing arepresentation method for representing an object or a shape referring todrawings.

FIG. 13 is blocks illustrating a configuration of the image processingdevice used to realize the representation method for representing anobject or a shape according to the second embodiment of this invention.Differences from the image processing device of FIG. 1 are in that theimage processing device includes, in place of the contour curvaturecalculation unit 106, a contour occupied area calculation unit 111, and,in place of the contour arc length/curvature/position output unit 108, acontour arc length/occupied area/position output unit 112. Resultingfrom these changes, the contour arc length/curvature/position storageunit 202 is renamed to a contour arc length/occupied area/positioninformation storage unit 203. Further, even with the same names, inorder to respond to the changes, there are elements having functionsdifferent from those of the image processing device of FIG. 1. Adescription is now given of different points from the image processingdevice of FIG. 1.

The contour occupied area calculation unit 111 calculates an area (alsoreferred to as contour occupied area) characteristic to each of thedivided contour lines divided by the contour division unit 104. Theaffine curvature used in the first embodiment drastically changes invalue, and is difficult to handle. In contrast, the contour occupiedarea is limited in a range of change, is easy to handle, and facilitatesrecognition of an object or a shape.

On this occasion, the characteristic area is, for example, an areadetermined depending on each divided contour line 20001 as illustratedin FIG. 14. In other words, the characteristic area is an areacalculated by using points that can be determined by the shape of eachdivided contour line. In detail, an area of a quadrangle obtained byconnecting four points, which are both end points 20002 and 20003 of thedivided contour line 20001, and points 20004 and 20005 which equallydivide (in this case, into three equal parts) a contour arc lengthrepresented by an affine arc length of the divided contour line 20001,may be considered as the characteristic area. An area of a regionenclosed by a line connecting the both end points 20002 and 20003 of thedivided contour line 20001 with each other, and the divided contour line20001 may be considered as the characteristic area. However, the area ofthe region enclosed by the four points 20002-20005 is preferably used.These four points are constituted by the end points which areinvariables with respect to the projective transformation and the twopoints which divide the affine arc length, which is an invariable withrespect to the affine transformation, into the three equal parts, andthe area enclosed by the four points is thus an invariable with respectto the equivalent affine transformation, and is an amount robust againstthe geometric transformation. The number of divisions of the contour arclength represented by the affine arc length should be equal to or morethan two (equal to or more than two equal divisions). If the number ofdivisions is two, the contour occupied area calculation unit 111determines the area of a triangle obtained by connecting both the endpoints 20002 and 20003 of the divided contour line 20001 and onedivision point with each other as the contour occupied area.

By determining a contour occupied area for each of the divided contourlines, if the number of the divided contour lines are two or more, arelative relationship thereamong can be determined, which is effectivefor recognition in a case where only a more partial shape than that inthe first embodiment can be detected.

Both the contour arc length and the contour occupied area areinvariables with respect to the equivalent affine transformation, and bytaking a ratio of one to the other thereof, an invariable with respectto the affine geometric transformation accompanying scaling can beprovided.

The contour arc length/occupied area/position output unit 112 outputsthe arc length information, the occupied area information, and theposition information respectively calculated by the contour arc lengthcalculation unit 105, the contour occupied area calculation unit 111,and the contour position calculation unit 107 to the contour arclength/occupied area/position information storage unit 203. The piecesof information output by the contour arc length/occupied area/positionoutput unit 112 are similar to the pieces of information (FIG. 8) outputby the contour arc length/curvature/position output unit 108. However,in place of the curvature information, the occupied area information isincluded.

The contour position calculation unit 107 may be different from that ofthe first embodiment, and may calculate a contour position by means ofan approach similar to that of deriving the occupied area by the contouroccupied area calculation unit 111. Employment of the approach enablesdescription of a positional relationship to be invariant with respect tothe affine geometric transformation.

Moreover, an invariable calculated from the positional relationship maybe added to the characteristic amounts. The invariable calculated fromthe positional relationship is, for example, an area enclosed by fourrepresentative points extracted from division points (inflection points)calculated by the contour division unit 104. This amount provides aninvariable with respect to the equivalent affine geometrictransformation. Further, by taking a ratio of one to the other of areasof two triangles divided by a diagonal line of the four points, aninvariable with respect to the affine geometric transformationaccompanying scaling is obtained.

Referring to FIG. 15, a description is now given of an operation of theimage processing device illustrated in FIG. 13. A different point fromthe operation of FIG. 12 is that, in place of Step S1009, the contouroccupied area calculation unit 111 calculates the occupied area (StepS1101). As a result, Step S1011 is also changed to Step S1102 where thecontour arc length/occupied area/position output unit 112 outputs thecontour length/occupied area/position information calculated in StepsS1008, S1101, and S1010.

According to this embodiment, by using, in place of the affinecurvature, the contour occupied area, in addition to the effects broughtabout by the first embodiment, the determined feature amount is easy tohandle, resulting in facilitation of recognition of the object or theshape.

A detailed description is now given of an image processing deviceaccording to a third embodiment of this invention used for realizing arepresentation method for representing an object or a shape referring todrawings.

FIG. 16 is blocks illustrating a configuration of the image processingdevice used to realize the representation method for representing anobject or a shape according to the third embodiment of this invention.Differences from the image processing device of FIG. 1 are in that aninflection point extraction unit 121, a contour direction calculationunit 122, and a coordinate transformation unit 124 are newly added aswell as in that, in place of the contour arc length/curvature/positionoutput unit 108, the image processing device includes the contour arclength/curvature/position/direction output unit 123. Further, even withthe same names, in order to respond to the changes, there are elementshaving functions different from those of the image processing device ofFIG. 1. A description is now given of different points from the imageprocessing device of FIG. 1.

The inflection point extraction unit 121 extracts inflection points on acontour by means of a method similar to that of the contour divisionunit 104 in the first embodiment. On this occasion, if an inflectionpoint is not observed, the number of extracted inflection points iszero.

The contour division unit 104 further divides a region (referred to ascontour segment) between inflection points (into contour sub-segments),which is different from the method of using an inflection point as acontour division point in the contour division unit 104 in the firstembodiment. The method of dividing the contour segment includes dividinga single contour segment so that, for example, the numbers of contoursub-segments in the single contour segment are the same, and so that arclengths of the contour sub-segments in the single contour segment areequal. The method of generating the contour sub-segments is not limitedto this approach, and any approach can be used. As a result, the devicessubsequent to the contour arc length calculation unit 105 carry outprocessing for the respective contour sub-segments.

The contour direction calculation unit 122 is a processing unit newlyadded to the first embodiment. In the first embodiment, the contourposition calculation unit 107 may calculate the direction, but in thethird embodiment, the contour direction calculation unit 122 calculatesthe direction. As a result, the contour position calculation unit 107calculates a position different from the direction information. Forexample, by using the Cartesian coordinate system, to identify atwo-dimensional position in an image, a position can be calculated. As aresult of addition of the contour direction calculation unit 122, thecontour arc

-   length/curvature/position output unit 108 is changed to the contour    arc-   length/curvature/position/direction output unit 123, which outputs,    in addition to the contour arc-   length/curvature/position information, newly the direction, and    similarly, the contour arc-   length/curvature/position information storage unit 202 is changed to    the contour arc-   length/curvature/position/direction information storage unit 204.

The coordinate transformation unit 124 properly transforms thecoordinates of the image acquired by the image information acquisitionunit 101 so that the coordinates correspond to each of images includedin the image information storage unit 201. Moreover, the coordinatetransformation unit 124 also carries out the coordinate transformationfor the contour arc

-   length/curvature/position/direction information output by the    contour arc-   length/curvature/position/direction output unit 123. The coordinate    transformation is carried out so that the contour arc    length/curvature/position/direction information output for the image    acquired by the image information acquisition unit 101 most closely    approximates the contour arc length/curvature/position/direction    information corresponding to each of the images included in the    image information storage unit 201. For the coordinate    transformation, for example, linear transformations such as the    translation, the rotation, the scaling, the affine geometric    transformation, and the projective geometric transformation in the    two-dimensional Cartesian coordinate system can be used. As the    transformation means used for the coordinate transformation, any    transformation means may be used irrespective of whether the    transformation means is linear transformation means or nonlinear    transformation means.

Referring to FIG. 17, a description is now given of an operation of theimage processing device illustrated in FIG. 16. A different point fromthe operation of FIG. 12 is that, after Step S1010, the contourdirection calculation unit 122 calculates the contour direction (StepS1201). As a result, Step S1011 is also changed to Step S1202 where thecontour arc length/curvature/position/direction output unit 123 outputsthe arc length/curvature/position/direction information calculated inSteps S1008, S1009, S1010, and S1201. Further, in FIG. 17, the partialcontours divided in Step S1007 correspond to the sub-segments. Moreover,the search for images in Step S1014 accompanies the coordinatetransformation by the coordinate transformation unit 124.

According to this embodiment, by dividing a counter on the two stagescorresponding to the segment and the sub-segment, and by using thecoordinate transformation, in addition to the effects of the firstembodiment, the following effects are expected.

First, the segment contributes to a high-speed search for correspondingpoints in two images.

Then, the sub-segment can describe, in detail, characteristics of alocal contour in the segment (between inflection points).

Finally, the coordinate transformation contributes to robust imagerecognition regardless of a distortion of an image.

This invention has now been described by way of several embodiments, butthis invention is not limited to those embodiments and variousmodifications and variations may be made without departing from thescope of the invention.

For example, in the above-mentioned embodiments, the combination betweenthe contour arc length calculation unit 105 and the contour curvaturecalculation unit 106 or the contour occupied area calculation unit 111is exemplified, but in place of the combination, a combination betweenthe contour curvature calculation unit 106 and the contour occupied areacalculation unit 111 may be used. Further, the contour directioncalculation unit 122 may be combined. In these cases, other relatedcomponents are, depending on the combination, changed as appropriate.

Moreover, according to the above-mentioned embodiments, though adescription is given of the image processing device dedicated to theimage processing, by controlling a general computer to execute a programto carry out the above-mentioned processing, the computer may beoperated as the image processing device. In other words, this inventioncan be provided as the program which controls the computer to carry outthe above-mentioned image processing method. Alternatively, the programcan be provided as a computer-readable, non-transitory informationrecording medium having the program stored thereon. If a generalcomputer is used to be operated as the image processing device of FIG.1, for example, the computer needs to include at least the control unit10, the memory 20, and the input/output unit 30. The memory 20 storesthe program, and serves as the image information storage unit 201 andthe contour arc length/curvature/position information storage unit 202.Moreover, the control unit 10 serves, by executing the program, as theimage information acquisition unit 101 to the image determination unit109. Depending on necessity, a read device for reading the program fromthe information recording medium, and transfers the read program to thememory 20 or the like is provided.

Moreover, a part or an entirety of the above-mentioned embodiments maybe described as the following notes, but this invention is not limitedthereto.

-   (Note 1) An image processing method, including: identifying, by    processing image data, a contour line of an object included in an    image represented by the image data; smoothing the contour line    stepwise to obtain smoothed contour lines on a plurality of stages;    determining a feature amount for each of the smoothed contour lines    on the plurality of stages; and determining, based on the determined    feature amount of the smoothed contour line on each of the stages    and a feature amount corresponding to each of the stages determined    in advance for an object for comparison, a degree of similarity of    the object and the object for comparison to each other.-   (Note 2) An image processing method as described in Note 1, in which    the step of determining the feature amount includes dividing each of    the smoothed contour lines on the plurality of stages into one or    more partial contour lines, and determining the feature amount for    each of the divided contour lines.-   (Note 3) An image processing method as described in Note 2, in which    the feature amount includes information on a position and a degree    of curvature of each of the partial contour lines.-   (Note 4) An image processing method as described in Note 3, in which    the information on the degree of curvature is an area of a region    enclosed by straight lines connecting a plurality of points existing    on the partial contour line, or a plurality of points defined    depending on a shape of the partial contour line with each other.-   (Note 5) An image processing method as described in Note 3, in which    the information on the degree of curvature is a combination of two    or more of an area of a region enclosed by straight lines connecting    a plurality of points existing on the partial contour line, or a    plurality of points defined depending on a shape of the partial    contour line with each other, an arc length of the partial contour    line, and a curvature of the partial contour line.-   (Note 6) An image processing method as described in Note 5, in which    the information on the degree of curvature of the curve is    represented by the following two: an arc length and a curvature of    the curve.-   (Note 7) An image processing method as described in Note 6, in which    the arc length and the curvature are respectively an affine arc    length and an affine curvature.-   (Note 8) An image processing method as described in any one of Notes    4 to 7, in which the plurality of points existing on the partial    contour line, or the plurality of points defined depending on the    shape of the partial contour line are at invariant positions with    respect to an affine geometric transformation.-   (Note 9) An image processing method as described in any one of Notes    2 to 8, in which a division point at which the dividing into the one    or more partial contour lines is carried out includes an inflection    point at which a sign of a curvature on the contour line changes.-   (Note 10) An image processing method as described in any one of    Notes 2 to 9, in which a method used for the dividing into the one    or more partial contour lines uses a division method on two stages    involving carrying out global division based on inflection points at    which a sign of a curvature on the contour line changes, and further    locally dividing a region between the inflection points.-   (Note 11) An image processing method as described in Note 4 or 5, in    which the area is an area of a region defined by end points on both    sides of the partial contour line, and division points when the    partial contour line is divided into a plurality of parts based on    an affine arc length.-   (Note 12) An image processing method as described in any one of    Notes 3 to 11, in which the information on the position of the    partial contour line is an invariable with respect to an affine    geometric transformation.-   (Note 13) An image processing method as described in any one of    Notes 3 to 12, in which the information on the position of partial    contour line is a number assigned in sequence along the contour line    or coordinates.-   (Note 14) An image processing method as described in any one of    Notes 1 to 13, in which the feature amount further includes    information on a direction of each of the partial contour lines.-   (Note 15) An image processing device for carrying out the image    processing method as described in any one of Notes 1 to 14.-   (Note 16) A program for controlling a computer to carry out the    image processing method as described in any one of Notes 1 to 15.

INDUSTRIAL APPLICABILITY

This invention can be used for applications such as, in recognition ofan object in a general image or motion image, search for a desired imageand classification of an image. In particular, this invention can beused for applications such as search and classification of similar butdifferent images.

This application claims priority from Japanese Patent Application No.2010-263877, filed on Nov. 26, 2010, and Japanese Patent Application No.2011-213005, filed on Sep. 28, 2011, the entire disclosure of which isincorporated herein by reference.

REFERENCE SIGNS LIST

10 control unit

20 memory

30 input/output unit

101 image information acquisition unit

102 contour extraction unit

103 contour smoothing unit

104 contour division unit

105 contour arc length calculation unit

106 contour curvature calculation unit

107 contour position calculation unit

108 contour arc length/curvature/position output unit

109 image determination unit

111 contour occupied area calculation unit

112 contour arc length/occupied area/position output unit

121 inflection point extraction unit

122 contour direction calculation unit

123 contour arc length/curvature/position/direction output unit

124 coordinate transformation unit

204 contour arc length/curvature/position/direction information storageunit

201 image information storage unit

202 contour arc length/curvature/position information storage unit

203 contour arc length/occupied area/position information storage unit

20001 divided contour line

20002, 20003 end point

20004, 20005 point which equally divides contour arc length representedby affine arc length

1. An information representation method for representing an object or ashape, comprising: dividing a contour shape of an entirety or a part ofthe object or the shape into one or a plurality of curves; andrepresenting the contour shape by parameters including a degree ofcurvature and a positional relationship of each curve obtained by thedividing.
 2. An information representation method for an object or ashape according to claim 1, wherein the degree of curvature of the curveis represented by an area calculated by using a plurality of points onthe curve or a plurality of points in positions which are determinableby a shape of the curve.
 3. An information representation method for anobject or a shape according to claim 1, wherein the degree of curvatureof the curve is represented by any two or more of an area calculated byusing a plurality of points on the curve or a plurality of points inpositions which are determinable by a shape of the curve, an arc lengthof the curve, and a curvature of the curve.
 4. An informationrepresentation method for an object or a shape according to claim 1,wherein the degree of curvature of the curve is represented by thefollowing two: an arc length of the curve and a curvature of the curve.5. An information representation method for an object or a shapeaccording to claim 1, wherein an arc length of the curve and a curvatureof the curve are respectively an affine arc length and an affinecurvature.
 6. An information representation method for an object or ashape according to claim 1, wherein positions of a plurality of pointson the curve or a plurality of points in positions which aredeterminable by the shape of the curve are invariant positions withrespect to an affine geometric transformation.
 7. An informationrepresentation method for an object or a shape according to claim 1,wherein a division point at which the division is carried out includesan inflection point at which a sign of a curvature on a contour changes.8. An information representation method for an object or a shapeaccording to claim 1, wherein a method used for the dividing uses adivision method on two stages involving: carrying out global divisionbased on inflection points at which a sign of a curvature on a contourchanges; and further locally dividing a region between the inflectionpoints.
 9. An information representation method for an object or a shapeaccording to claim 1, wherein an area defined by the curve is derived byusing at least three points out of division points for dividing thecurve into a plurality of parts based on an affine arc length of thecurve as an index, and end points of the curve.
 10. An informationrepresentation method for an object or a shape according to claim 1,wherein a positional relationship between the one or the plurality ofcurves is represented by an invariable with respect to an affinegeometric transformation.
 11. An information representation method foran object or a shape according to claim 1, wherein a positionalrelationship of the curve is a positional relationship among the one orthe plurality of curves obtained by the dividing or a positionalrelationship among the one or the plurality of curves obtained by thedividing in a plurality of the contour shapes.
 12. An informationrepresentation method for an object or a shape according to claim 1,wherein the positional relationship of the curve is represented by oneor more indices selected from objective indices including a sequence orcoordinates of the each curve.
 13. An information representation methodfor an object or a shape according to claim 1, wherein the each curveobtained by the dividing is represented by parameters including andirection in addition to the degree of curvature and the positionalrelationship of the curve.
 14. An information representation method foran object or a shape according to claim 1, wherein the each curveobtained by the dividing is represented by a plurality of pieces ofstratified information.
 15. An information representation method for anobject or a shape according to claim 1, wherein, when two of the objectsor the shapes are matched to each other, the information representationmethod accompanies a geometric transformation.
 16. A system forrepresenting information on an object or a shape, comprising: dividingmeans for dividing a contour shape of an entirety or a part of theobject or the shape into one or a plurality of curves; and parametercalculation means for representing the contour shape by parametersincluding a degree of curvature and a positional relationship of eachcurve obtained by the division.
 17. A computer-readable programrecording medium which stores a program for causing a computer toexecute the steps of: dividing a contour shape of an entirety or a partof an object or a shape into one or a plurality of curves; andrepresenting the contour shape by parameters including a degree ofcurvature and a positional relationship of each curve obtained by thedividing.
 18. A representation method for an object shape comprising:dividing, by processing image data representing an image including anobject, at least a part of a contour line of the object into one or morecurves; and representing each of the one or more curves by a firstparameter representing a degree of curvature and a second parameterrepresenting a position.